(2w+1)(w)=28

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Solution for (2w+1)(w)=28 equation:


Simplifying
(2w + 1)(w) = 28

Reorder the terms:
(1 + 2w)(w) = 28

Reorder the terms for easier multiplication:
w(1 + 2w) = 28
(1 * w + 2w * w) = 28
(1w + 2w2) = 28

Solving
1w + 2w2 = 28

Solving for variable 'w'.

Reorder the terms:
-28 + 1w + 2w2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 1w + 2w2 = 0

Factor a trinomial.
(-4 + -1w)(7 + -2w) = 0

Subproblem 1

Set the factor '(-4 + -1w)' equal to zero and attempt to solve: Simplifying -4 + -1w = 0 Solving -4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1w = 0 + 4 -1w = 0 + 4 Combine like terms: 0 + 4 = 4 -1w = 4 Divide each side by '-1'. w = -4 Simplifying w = -4

Subproblem 2

Set the factor '(7 + -2w)' equal to zero and attempt to solve: Simplifying 7 + -2w = 0 Solving 7 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2w = 0 + -7 -2w = 0 + -7 Combine like terms: 0 + -7 = -7 -2w = -7 Divide each side by '-2'. w = 3.5 Simplifying w = 3.5

Solution

w = {-4, 3.5}

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